nhaliday + estimate   95

An adaptability limit to climate change due to heat stress
Despite the uncertainty in future climate-change impacts, it is often assumed that humans would be able to adapt to any possible warming. Here we argue that heat stress imposes a robust upper limit to such adaptation. Peak heat stress, quantified by the wet-bulb temperature TW, is surprisingly similar across diverse climates today. TW never exceeds 31 °C. Any exceedence of 35 °C for extended periods should induce hyperthermia in humans and other mammals, as dissipation of metabolic heat becomes impossible. While this never happens now, it would begin to occur with global-mean warming of about 7 °C, calling the habitability of some regions into question. With 11–12 °C warming, such regions would spread to encompass the majority of the human population as currently distributed. Eventual warmings of 12 °C are possible from fossil fuel burning. One implication is that recent estimates of the costs of unmitigated climate change are too low unless the range of possible warming can somehow be narrowed. Heat stress also may help explain trends in the mammalian fossil record.

Trajectories of the Earth System in the Anthropocene: http://www.pnas.org/content/early/2018/07/31/1810141115
We explore the risk that self-reinforcing feedbacks could push the Earth System toward a planetary threshold that, if crossed, could prevent stabilization of the climate at intermediate temperature rises and cause continued warming on a “Hothouse Earth” pathway even as human emissions are reduced. Crossing the threshold would lead to a much higher global average temperature than any interglacial in the past 1.2 million years and to sea levels significantly higher than at any time in the Holocene. We examine the evidence that such a threshold might exist and where it might be.
study  org:nat  environment  climate-change  humanity  existence  risk  futurism  estimate  physics  thermo  prediction  temperature  nature  walls  civilization  flexibility  rigidity  embodied  multi  manifolds  plots  equilibrium  phase-transition  oscillation  comparison  complex-systems  earth 
august 2018 by nhaliday
Theory of Self-Reproducing Automata - John von Neumann
Fourth Lecture: THE ROLE OF HIGH AND OF EXTREMELY HIGH COMPLICATION

Comparisons between computing machines and the nervous systems. Estimates of size for computing machines, present and near future.

Estimates for size for the human central nervous system. Excursus about the “mixed” character of living organisms. Analog and digital elements. Observations about the “mixed” character of all componentry, artificial as well as natural. Interpretation of the position to be taken with respect to these.

Evaluation of the discrepancy in size between artificial and natural automata. Interpretation of this discrepancy in terms of physical factors. Nature of the materials used.

The probability of the presence of other intellectual factors. The role of complication and the theoretical penetration that it requires.

Questions of reliability and errors reconsidered. Probability of individual errors and length of procedure. Typical lengths of procedure for computing machines and for living organisms--that is, for artificial and for natural automata. Upper limits on acceptable probability of error in individual operations. Compensation by checking and self-correcting features.

Differences of principle in the way in which errors are dealt with in artificial and in natural automata. The “single error” principle in artificial automata. Crudeness of our approach in this case, due to the lack of adequate theory. More sophisticated treatment of this problem in natural automata: The role of the autonomy of parts. Connections between this autonomy and evolution.

- 10^10 neurons in brain, 10^4 vacuum tubes in largest computer at time
- machines faster: 5 ms from neuron potential to neuron potential, 10^-3 ms for vacuum tubes

https://en.wikipedia.org/wiki/John_von_Neumann#Computing
pdf  article  papers  essay  nibble  math  cs  computation  bio  neuro  neuro-nitgrit  scale  magnitude  comparison  acm  von-neumann  giants  thermo  phys-energy  speed  performance  time  density  frequency  hardware  ems  efficiency  dirty-hands  street-fighting  fermi  estimate  retention  physics  interdisciplinary  multi  wiki  links  people  🔬  atoms  automata  duplication  iteration-recursion  turing  complexity  measure  nature  technology  complex-systems  bits  information-theory  circuits  robust  structure  composition-decomposition  evolution  mutation  axioms  analogy  thinking  input-output  hi-order-bits  coding-theory  flexibility  rigidity 
april 2018 by nhaliday
Existential Risks: Analyzing Human Extinction Scenarios
https://twitter.com/robinhanson/status/981291048965087232
https://archive.is/dUTD5
Would you endorse choosing policy to max the expected duration of civilization, at least as a good first approximation?
Can anyone suggest a different first approximation that would get more votes?

https://twitter.com/robinhanson/status/981335898502545408
https://archive.is/RpygO
How useful would it be to agree on a relatively-simple first-approximation observable-after-the-fact metric for what we want from the future universe, such as total life years experienced, or civilization duration?

We're Underestimating the Risk of Human Extinction: https://www.theatlantic.com/technology/archive/2012/03/were-underestimating-the-risk-of-human-extinction/253821/
An Oxford philosopher argues that we are not adequately accounting for technology's risks—but his solution to the problem is not for Luddites.

Anderson: You have argued that we underrate existential risks because of a particular kind of bias called observation selection effect. Can you explain a bit more about that?

Bostrom: The idea of an observation selection effect is maybe best explained by first considering the simpler concept of a selection effect. Let's say you're trying to estimate how large the largest fish in a given pond is, and you use a net to catch a hundred fish and the biggest fish you find is three inches long. You might be tempted to infer that the biggest fish in this pond is not much bigger than three inches, because you've caught a hundred of them and none of them are bigger than three inches. But if it turns out that your net could only catch fish up to a certain length, then the measuring instrument that you used would introduce a selection effect: it would only select from a subset of the domain you were trying to sample.

Now that's a kind of standard fact of statistics, and there are methods for trying to correct for it and you obviously have to take that into account when considering the fish distribution in your pond. An observation selection effect is a selection effect introduced not by limitations in our measurement instrument, but rather by the fact that all observations require the existence of an observer. This becomes important, for instance, in evolutionary biology. For instance, we know that intelligent life evolved on Earth. Naively, one might think that this piece of evidence suggests that life is likely to evolve on most Earth-like planets. But that would be to overlook an observation selection effect. For no matter how small the proportion of all Earth-like planets that evolve intelligent life, we will find ourselves on a planet that did. Our data point-that intelligent life arose on our planet-is predicted equally well by the hypothesis that intelligent life is very improbable even on Earth-like planets as by the hypothesis that intelligent life is highly probable on Earth-like planets. When it comes to human extinction and existential risk, there are certain controversial ways that observation selection effects might be relevant.
bostrom  ratty  miri-cfar  skunkworks  philosophy  org:junk  list  top-n  frontier  speedometer  risk  futurism  local-global  scale  death  nihil  technology  simulation  anthropic  nuclear  deterrence  environment  climate-change  arms  competition  ai  ai-control  genetics  genomics  biotech  parasites-microbiome  disease  offense-defense  physics  tails  network-structure  epidemiology  space  geoengineering  dysgenics  ems  authoritarianism  government  values  formal-values  moloch  enhancement  property-rights  coordination  cooperate-defect  flux-stasis  ideas  prediction  speculation  humanity  singularity  existence  cybernetics  study  article  letters  eden-heaven  gedanken  multi  twitter  social  discussion  backup  hanson  metrics  optimization  time  long-short-run  janus  telos-atelos  poll  forms-instances  threat-modeling  selection  interview  expert-experience  malthus  volo-avolo  intel  leviathan  drugs  pharma  data  estimate  nature  longevity  expansionism  homo-hetero  utopia-dystopia 
march 2018 by nhaliday
Stein's example - Wikipedia
Stein's example (or phenomenon or paradox), in decision theory and estimation theory, is the phenomenon that when three or more parameters are estimated simultaneously, there exist combined estimators more accurate on average (that is, having lower expected mean squared error) than any method that handles the parameters separately. It is named after Charles Stein of Stanford University, who discovered the phenomenon in 1955.[1]

An intuitive explanation is that optimizing for the mean-squared error of a combined estimator is not the same as optimizing for the errors of separate estimators of the individual parameters. In practical terms, if the combined error is in fact of interest, then a combined estimator should be used, even if the underlying parameters are independent; this occurs in channel estimation in telecommunications, for instance (different factors affect overall channel performance). On the other hand, if one is instead interested in estimating an individual parameter, then using a combined estimator does not help and is in fact worse.

...

Many simple, practical estimators achieve better performance than the ordinary estimator. The best-known example is the James–Stein estimator, which works by starting at X and moving towards a particular point (such as the origin) by an amount inversely proportional to the distance of X from that point.
nibble  concept  levers  wiki  reference  acm  stats  probability  decision-theory  estimate  distribution  atoms 
february 2018 by nhaliday
Information Processing: US Needs a National AI Strategy: A Sputnik Moment?
FT podcasts on US-China competition and AI: http://infoproc.blogspot.com/2018/05/ft-podcasts-on-us-china-competition-and.html

A new recommended career path for effective altruists: China specialist: https://80000hours.org/articles/china-careers/
Our rough guess is that it would be useful for there to be at least ten people in the community with good knowledge in this area within the next few years.

By “good knowledge” we mean they’ve spent at least 3 years studying these topics and/or living in China.

We chose ten because that would be enough for several people to cover each of the major areas listed (e.g. 4 within AI, 2 within biorisk, 2 within foreign relations, 1 in another area).

AI Policy and Governance Internship: https://www.fhi.ox.ac.uk/ai-policy-governance-internship/

https://www.fhi.ox.ac.uk/deciphering-chinas-ai-dream/
https://www.fhi.ox.ac.uk/wp-content/uploads/Deciphering_Chinas_AI-Dream.pdf
Deciphering China’s AI Dream
The context, components, capabilities, and consequences of
China’s strategy to lead the world in AI

Europe’s AI delusion: https://www.politico.eu/article/opinion-europes-ai-delusion/
Brussels is failing to grasp threats and opportunities of artificial intelligence.
By BRUNO MAÇÃES

When the computer program AlphaGo beat the Chinese professional Go player Ke Jie in a three-part match, it didn’t take long for Beijing to realize the implications.

If algorithms can already surpass the abilities of a master Go player, it can’t be long before they will be similarly supreme in the activity to which the classic board game has always been compared: war.

As I’ve written before, the great conflict of our time is about who can control the next wave of technological development: the widespread application of artificial intelligence in the economic and military spheres.

...

If China’s ambitions sound plausible, that’s because the country’s achievements in deep learning are so impressive already. After Microsoft announced that its speech recognition software surpassed human-level language recognition in October 2016, Andrew Ng, then head of research at Baidu, tweeted: “We had surpassed human-level Chinese recognition in 2015; happy to see Microsoft also get there for English less than a year later.”

...

One obvious advantage China enjoys is access to almost unlimited pools of data. The machine-learning technologies boosting the current wave of AI expansion are as good as the amount of data they can use. That could be the number of people driving cars, photos labeled on the internet or voice samples for translation apps. With 700 or 800 million Chinese internet users and fewer data protection rules, China is as rich in data as the Gulf States are in oil.

How can Europe and the United States compete? They will have to be commensurately better in developing algorithms and computer power. Sadly, Europe is falling behind in these areas as well.

...

Chinese commentators have embraced the idea of a coming singularity: the moment when AI surpasses human ability. At that point a number of interesting things happen. First, future AI development will be conducted by AI itself, creating exponential feedback loops. Second, humans will become useless for waging war. At that point, the human mind will be unable to keep pace with robotized warfare. With advanced image recognition, data analytics, prediction systems, military brain science and unmanned systems, devastating wars might be waged and won in a matter of minutes.

...

The argument in the new strategy is fully defensive. It first considers how AI raises new threats and then goes on to discuss the opportunities. The EU and Chinese strategies follow opposite logics. Already on its second page, the text frets about the legal and ethical problems raised by AI and discusses the “legitimate concerns” the technology generates.

The EU’s strategy is organized around three concerns: the need to boost Europe’s AI capacity, ethical issues and social challenges. Unfortunately, even the first dimension quickly turns out to be about “European values” and the need to place “the human” at the center of AI — forgetting that the first word in AI is not “human” but “artificial.”

https://twitter.com/mr_scientism/status/983057591298351104
https://archive.is/m3Njh
US military: "LOL, China thinks it's going to be a major player in AI, but we've got all the top AI researchers. You guys will help us develop weapons, right?"

US AI researchers: "No."

US military: "But... maybe just a computer vision app."

US AI researchers: "NO."

https://www.theverge.com/2018/4/4/17196818/ai-boycot-killer-robots-kaist-university-hanwha
https://www.nytimes.com/2018/04/04/technology/google-letter-ceo-pentagon-project.html
https://twitter.com/mr_scientism/status/981685030417326080
https://archive.is/3wbHm
AI-risk was a mistake.
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february 2018 by nhaliday
Sex, Drugs, and Bitcoin: How Much Illegal Activity Is Financed Through Cryptocurrencies? by Sean Foley, Jonathan R. Karlsen, Tālis J. Putniņš :: SSRN
Cryptocurrencies are among the largest unregulated markets in the world. We find that approximately one-quarter of bitcoin users and one-half of bitcoin transactions are associated with illegal activity. Around $72 billion of illegal activity per year involves bitcoin, which is close to the scale of the US and European markets for illegal drugs. The illegal share of bitcoin activity declines with mainstream interest in bitcoin and with the emergence of more opaque cryptocurrencies. The techniques developed in this paper have applications in cryptocurrency surveillance. Our findings suggest that cryptocurrencies are transforming the way black markets operate by enabling “black e-commerce.”
study  economics  law  leviathan  bitcoin  cryptocurrency  crypto  impetus  scale  markets  civil-liberty  randy-ayndy  crime  criminology  measurement  estimate  pro-rata  money  monetary-fiscal  crypto-anarchy  drugs  internet  tradecraft  opsec  security 
february 2018 by nhaliday
Team *Decorations Until Epiphany* on Twitter: "@RoundSqrCupola maybe just C https://t.co/SFPXb3qrAE"
https://archive.is/k0fsS
Remember ‘BRICs’? Now it’s just ICs.
--
maybe just C
Solow predicts that if 2 countries have the same TFP, then the poorer nation should grow faster. But poorer India grows more slowly than China.

Solow thinking leads one to suspect India has substantially lower TFP.

Recent growth is great news, but alas 5 years isn't the long run!

FWIW under Solow conditional convergence assumptions--historically robust--the fact that a country as poor as India grows only a few % faster than the world average is a sign they'll end up poorer than S Europe.

see his spreadsheet here: http://mason.gmu.edu/~gjonesb/SolowForecast.xlsx
spearhead  econotariat  garett-jones  unaffiliated  twitter  social  discussion  india  asia  china  economics  macro  growth-econ  econ-metrics  wealth  wealth-of-nations  convergence  world  developing-world  trends  time-series  cjones-like  prediction  multi  backup  the-bones  long-short-run  europe  mediterranean  comparison  simulation  econ-productivity  great-powers  thucydides  broad-econ  pop-diff  microfoundations  🎩  marginal  hive-mind  rindermann-thompson  hari-seldon  tools  calculator  estimate 
december 2017 by nhaliday
galaxy - How do astronomers estimate the total mass of dust in clouds and galaxies? - Astronomy Stack Exchange
Dust absorbs stellar light (primarily in the ultraviolet), and is heated up. Subsequently it cools by emitting infrared, "thermal" radiation. Assuming a dust composition and grain size distribution, the amount of emitted IR light per unit dust mass can be calculated as a function of temperature. Observing the object at several different IR wavelengths, a Planck curve can be fitted to the data points, yielding the dust temperature. The more UV light incident on the dust, the higher the temperature.

The result is somewhat sensitive to the assumptions, and thus the uncertainties are sometimes quite large. The more IR data points obtained, the better. If only one IR point is available, the temperature cannot be calculated. Then there's a degeneracy between incident UV light and the amount of dust, and the mass can only be estimated to within some orders of magnitude (I think).
nibble  q-n-a  overflow  space  measurement  measure  estimate  physics  electromag  visuo  methodology 
december 2017 by nhaliday
Tax Evasion and Inequality
This paper attempts to estimate the size and distribution of tax evasion in rich countries. We combine stratified random audits—the key source used to study tax evasion so far—with new micro-data leaked from two large offshore financial institutions, HSBC Switzerland (“Swiss leaks”) and Mossack Fonseca (“Panama Papers”). We match these data to population-wide wealth records in Norway, Sweden, and Denmark. We find that tax evasion rises sharply with wealth, a phenomenon that random audits fail to capture. On average about 3% of personal taxes are evaded in Scandinavia, but this figure rises to about 30% in the top 0.01% of the wealth distribution, a group that includes households with more than $40 million in net wealth. A simple model of the supply of tax evasion services can explain why evasion rises steeply with wealth. Taking tax evasion into account increases the rise in inequality seen in tax data since the 1970s markedly, highlighting the need to move beyond tax data to capture income and wealth at the top, even in countries where tax compliance is generally high. We also find that after reducing tax evasion—by using tax amnesties—tax evaders do not legally avoid taxes more. This result suggests that fighting tax evasion can be an effective way to collect more tax revenue from the ultra-wealthy.

Figure 1

America’s unreported economy: measuring the size, growth and determinants of income tax evasion in the U.S.: https://link.springer.com/article/10.1007/s10611-011-9346-x
This study empirically investigates the extent of noncompliance with the tax code and examines the determinants of federal income tax evasion in the U.S. Employing a refined version of Feige’s (Staff Papers, International Monetary Fund 33(4):768–881, 1986, 1989) General Currency Ratio (GCR) model to estimate a time series of unreported income as our measure of tax evasion, we find that 18–23% of total reportable income may not properly be reported to the IRS. This gives rise to a 2009 “tax gap” in the range of $390–$540 billion. As regards the determinants of tax noncompliance, we find that federal income tax evasion is an increasing function of the average effective federal income tax rate, the unemployment rate, the nominal interest rate, and per capita real GDP, and a decreasing function of the IRS audit rate. Despite important refinements of the traditional currency ratio approach for estimating the aggregate size and growth of unreported economies, we conclude that the sensitivity of the results to different benchmarks, imperfect data sources and alternative specifying assumptions precludes obtaining results of sufficient accuracy and reliability to serve as effective policy guides.
pdf  study  economics  micro  evidence-based  data  europe  nordic  scale  class  compensation  money  monetary-fiscal  political-econ  redistribution  taxes  madisonian  inequality  history  mostly-modern  natural-experiment  empirical  🎩  cocktail  correlation  models  supply-demand  GT-101  crooked  elite  vampire-squid  nationalism-globalism  multi  pro-rata  usa  time-series  trends  world-war  cold-war  government  todo  planning  long-term  trivia  law  crime  criminology  estimate  speculation  measurement  labor  macro  econ-metrics  wealth  stock-flow  time  density  criminal-justice  frequency  dark-arts  traces  evidence 
october 2017 by nhaliday
Caught in the act | West Hunter
The fossil record is sparse. Let me try to explain that. We have at most a few hundred Neanderthal skeletons, most in pretty poor shape. How many Neanderthals ever lived? I think their population varied in size quite a bit – lowest during glacial maxima, probably highest in interglacials. Their degree of genetic diversity suggests an effective population size of ~1000, but that would be dominated by the low points (harmonic average). So let’s say 50,000 on average, over their whole range (Europe, central Asia, the Levant, perhaps more). Say they were around for 300,000 years, with a generation time of 30 years – 10,000 generations, for a total of five hundred million Neanderthals over all time. So one in a million Neanderthals ends up in a museum: one every 20 generations. Low time resolution!

So if anatomically modern humans rapidly wiped out Neanderthals, we probably couldn’t tell. In much the same way, you don’t expect to find the remains of many dinosaurs killed by the Cretaceous meteor impact (at most one millionth of one generation, right?), or of Columbian mammoths killed by a wave of Amerindian hunters. Sometimes invaders leave a bigger footprint: a bunch of cities burning down with no rebuilding tells you something. But even when you know that population A completely replaced population B, it can be hard to prove that just how it happened. After all, population A could have all committed suicide just before B showed up. Stranger things have happened – but not often.
west-hunter  scitariat  discussion  ideas  data  objektbuch  scale  magnitude  estimate  population  sapiens  archaics  archaeology  pro-rata  history  antiquity  methodology  volo-avolo  measurement  pop-structure  density  time  frequency  apollonian-dionysian  traces  evidence 
september 2017 by nhaliday
Atrocity statistics from the Roman Era
Christian Martyrs [make link]
Gibbon, Decline & Fall v.2 ch.XVI: < 2,000 k. under Roman persecution.
Ludwig Hertling ("Die Zahl de Märtyrer bis 313", 1944) estimated 100,000 Christians killed between 30 and 313 CE. (cited -- unfavorably -- by David Henige, Numbers From Nowhere, 1998)
Catholic Encyclopedia, "Martyr": number of Christian martyrs under the Romans unknown, unknowable. Origen says not many. Eusebius says thousands.

...

General population decline during The Fall of Rome: 7,000,000 [make link]
- Colin McEvedy, The New Penguin Atlas of Medieval History (1992)
- From 2nd Century CE to 4th Century CE: Empire's population declined from 45M to 36M [i.e. 9M]
- From 400 CE to 600 CE: Empire's population declined by 20% [i.e. 7.2M]
- Paul Bairoch, Cities and economic development: from the dawn of history to the present, p.111
- "The population of Europe except Russia, then, having apparently reached a high point of some 40-55 million people by the start of the third century [ca.200 C.E.], seems to have fallen by the year 500 to about 30-40 million, bottoming out at about 20-35 million around 600." [i.e. ca.20M]
- Francois Crouzet, A History of the European Economy, 1000-2000 (University Press of Virginia: 2001) p.1.
- "The population of Europe (west of the Urals) in c. AD 200 has been estimated at 36 million; by 600, it had fallen to 26 million; another estimate (excluding ‘Russia’) gives a more drastic fall, from 44 to 22 million." [i.e. 10M or 22M]

also:
The geometric mean of these two extremes would come to 4½ per day, which is a credible daily rate for the really bad years.

why geometric mean? can you get it as the MLE given min{X1, ..., Xn} and max{X1, ..., Xn} for {X_i} iid Poissons? some kinda limit? think it might just be a rule of thumb.

yeah, it's a rule of thumb. found it it his book (epub).
org:junk  data  let-me-see  scale  history  iron-age  mediterranean  the-classics  death  nihil  conquest-empire  war  peace-violence  gibbon  trivia  multi  todo  AMT  expectancy  heuristic  stats  ML-MAP-E  data-science  estimate  magnitude  population  demographics  database  list  religion  christianity  leviathan 
september 2017 by nhaliday
Medicine as a pseudoscience | West Hunter
The idea that venesection was a good thing, or at least not so bad, on the grounds that one in a few hundred people have hemochromatosis (in Northern Europe) reminds me of the people who don’t wear a seatbelt, since it would keep them from being thrown out of their convertible into a waiting haystack, complete with nubile farmer’s daughter. Daughters. It could happen. But it’s not the way to bet.

Back in the good old days, Charles II, age 53, had a fit one Sunday evening, while fondling two of his mistresses.

Monday they bled him (cupping and scarifying) of eight ounces of blood. Followed by an antimony emetic, vitriol in peony water, purgative pills, and a clyster. Followed by another clyster after two hours. Then syrup of blackthorn, more antimony, and rock salt. Next, more laxatives, white hellebore root up the nostrils. Powdered cowslip flowers. More purgatives. Then Spanish Fly. They shaved his head and stuck blistering plasters all over it, plastered the soles of his feet with tar and pigeon-dung, then said good-night.

...

Friday. The king was worse. He tells them not to let poor Nelly starve. They try the Oriental Bezoar Stone, and more bleeding. Dies at noon.

Most people didn’t suffer this kind of problem with doctors, since they never saw one. Charles had six. Now Bach and Handel saw the same eye surgeon, John Taylor – who blinded both of them. Not everyone can put that on his resume!

You may wonder how medicine continued to exist, if it had a negative effect, on the whole. There’s always the placebo effect – at least there would be, if it existed. Any real placebo effect is very small: I’d guess exactly zero. But there is regression to the mean. You see the doctor when you’re feeling worse than average – and afterwards, if he doesn’t kill you outright, you’re likely to feel better. Which would have happened whether you’d seen him or not, but they didn’t often do RCTs back in the day – I think James Lind was the first (1747).

Back in the late 19th century, Christian Scientists did better than others when sick, because they didn’t believe in medicine. For reasons I think mistaken, because Mary Baker Eddy rejected the reality of the entire material world, but hey, it worked. Parenthetically, what triggered all that New Age nonsense in 19th century New England? Hash?

This did not change until fairly recently. Sometime in the early 20th medicine, clinical medicine, what doctors do, hit break-even. Now we can’t do without it. I wonder if there are, or will be, other examples of such a pile of crap turning (mostly) into a real science.

good tweet: https://twitter.com/bowmanthebard/status/897146294191390720
The brilliant GP I've had for 35+ years has retired. How can I find another one who meets my requirements?

1 is overweight
2 drinks more than officially recommended amounts
3 has an amused, tolerant atitude to human failings
4 is well aware that we're all going to die anyway, & there are better or worse ways to die
5 has a healthy skeptical attitude to mainstream medical science
6 is wholly dismissive of "a|ternative” medicine
7 believes in evolution
8 thinks most diseases get better without intervention, & knows the dangers of false positives
9 understands the base rate fallacy

EconPapers: Was Civil War Surgery Effective?: http://econpapers.repec.org/paper/htrhcecon/444.htm
contra Greg Cochran:
To shed light on the subject, I analyze a data set created by Dr. Edmund Andrews, a Civil war surgeon with the 1st Illinois Light Artillery. Dr. Andrews’s data can be rendered into an observational data set on surgical intervention and recovery, with controls for wound location and severity. The data also admits instruments for the surgical decision. My analysis suggests that Civil War surgery was effective, and increased the probability of survival of the typical wounded soldier, with average treatment effect of 0.25-0.28.

Medical Prehistory: https://westhunt.wordpress.com/2016/03/14/medical-prehistory/
What ancient medical treatments worked?

https://westhunt.wordpress.com/2016/03/14/medical-prehistory/#comment-76878
In some very, very limited conditions, bleeding?
--
Bad for you 99% of the time.

https://westhunt.wordpress.com/2016/03/14/medical-prehistory/#comment-76947
Colchicine – used to treat gout – discovered by the Ancient Greeks.

https://westhunt.wordpress.com/2016/03/14/medical-prehistory/#comment-76973
Dracunculiasis (Guinea worm)
Wrap the emerging end of the worm around a stick and slowly pull it out.
(3,500 years later, this remains the standard treatment.)
https://en.wikipedia.org/wiki/Ebers_Papyrus

https://westhunt.wordpress.com/2016/03/14/medical-prehistory/#comment-76971
Some of the progress is from formal medicine, most is from civil engineering, better nutrition ( ag science and physical chemistry), less crowded housing.

Nurses vs doctors: https://westhunt.wordpress.com/2014/10/01/nurses-vs-doctors/
Medicine, the things that doctors do, was an ineffective pseudoscience until fairly recently. Until 1800 or so, they were wrong about almost everything. Bleeding, cupping, purging, the four humors – useless. In the 1800s, some began to realize that they were wrong, and became medical nihilists that improved outcomes by doing less. Some patients themselves came to this realization, as when Civil War casualties hid from the surgeons and had better outcomes. Sometime in the early 20th century, MDs reached break-even, and became an increasingly positive influence on human health. As Lewis Thomas said, medicine is the youngest science.

Nursing, on the other hand, has always been useful. Just making sure that a patient is warm and nourished when too sick to take care of himself has helped many survive. In fact, some of the truly crushing epidemics have been greatly exacerbated when there were too few healthy people to take care of the sick.

Nursing must be old, but it can’t have existed forever. Whenever it came into existence, it must have changed the selective forces acting on the human immune system. Before nursing, being sufficiently incapacitated would have been uniformly fatal – afterwards, immune responses that involved a period of incapacitation (with eventual recovery) could have been selectively favored.

when MDs broke even: https://westhunt.wordpress.com/2014/10/01/nurses-vs-doctors/#comment-58981
I’d guess the 1930s. Lewis Thomas thought that he was living through big changes. They had a working serum therapy for lobar pneumonia ( antibody-based). They had many new vaccines ( diphtheria in 1923, whopping cough in 1926, BCG and tetanus in 1927, yellow fever in 1935, typhus in 1937.) Vitamins had been mostly worked out. Insulin was discovered in 1929. Blood transfusions. The sulfa drugs, first broad-spectrum antibiotics, showed up in 1935.

DALYs per doctor: https://westhunt.wordpress.com/2018/01/22/dalys-per-doctor/
The disability-adjusted life year (DALY) is a measure of overall disease burden – the number of years lost. I’m wondering just much harm premodern medicine did, per doctor. How many healthy years of life did a typical doctor destroy (net) in past times?

...

It looks as if the average doctor (in Western medicine) killed a bunch of people over his career ( when contrasted with doing nothing). In the Charles Manson class.

Eventually the market saw through this illusion. Only took a couple of thousand years.

https://westhunt.wordpress.com/2018/01/22/dalys-per-doctor/#comment-100741
That a very large part of healthcare spending is done for non-health reasons. He has a chapter on this in his new book, also check out his paper “Showing That You Care: The Evolution of Health Altruism” http://mason.gmu.edu/~rhanson/showcare.pdf
--
I ran into too much stupidity to finish the article. Hanson’s a loon. For example when he talks about the paradox of blacks being more sentenced on drug offenses than whites although they use drugs at similar rate. No paradox: guys go to the big house for dealing, not for using. Where does he live – Mars?

I had the same reaction when Hanson parroted some dipshit anthropologist arguing that the stupid things people do while drunk are due to social expectations, not really the alcohol.
Horseshit.

I don’t think that being totally unable to understand everybody around you necessarily leads to deep insights.

https://westhunt.wordpress.com/2018/01/22/dalys-per-doctor/#comment-100744
What I’ve wondered is if there was anything that doctors did that actually was helpful and if perhaps that little bit of success helped them fool people into thinking the rest of it helped.
--
Setting bones. extracting arrows: spoon of Diocles. Colchicine for gout. Extracting the Guinea worm. Sometimes they got away with removing the stone. There must be others.
--
Quinine is relatively recent: post-1500. Obstetrical forceps also. Caesarean deliveries were almost always fatal to the mother until fairly recently.

Opium has been around for a long while : it works.

https://westhunt.wordpress.com/2018/01/22/dalys-per-doctor/#comment-100839
If pre-modern medicine was indeed worse than useless – how do you explain no one noticing that patients who get expensive treatments are worse off than those who didn’t?
--
were worse off. People are kinda dumb – you’ve noticed?
--
My impression is that while people may be “kinda dumb”, ancient customs typically aren’t.
Even if we assume that all people who lived prior to the 19th century were too dumb to make the rational observation, wouldn’t you expect this ancient practice to be subject to selective pressure?
--
Your impression is wrong. Do you think that there some slick reason for Carthaginians incinerating their first-born?

Theodoric of York, bloodletting: https://www.youtube.com/watch?v=yvff3TViXmY

details on blood-letting and hemochromatosis: https://westhunt.wordpress.com/2018/01/22/dalys-per-doctor/#comment-100746

Starting Over: https://westhunt.wordpress.com/2018/01/23/starting-over/
Looking back on it, human health would have … [more]
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august 2017 by nhaliday
Constitutive equation - Wikipedia
In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and approximates the response of that material to external stimuli, usually as applied fields or forces. They are combined with other equations governing physical laws to solve physical problems; for example in fluid mechanics the flow of a fluid in a pipe, in solid state physics the response of a crystal to an electric field, or in structural analysis, the connection between applied stresses or forces to strains or deformations.

Some constitutive equations are simply phenomenological; others are derived from first principles. A common approximate constitutive equation frequently is expressed as a simple proportionality using a parameter taken to be a property of the material, such as electrical conductivity or a spring constant. However, it is often necessary to account for the directional dependence of the material, and the scalar parameter is generalized to a tensor. Constitutive relations are also modified to account for the rate of response of materials and their non-linear behavior.[1] See the article Linear response function.
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august 2017 by nhaliday
Demography of the Roman Empire - Wikipedia
There are few recorded population numbers for the whole of antiquity, and those that exist are often rhetorical or symbolic. Unlike the contemporaneous Han Dynasty, no general census survives for the Roman Empire. The late period of the Roman Republic provides a small exception to this general rule: serial statistics for Roman citizen numbers, taken from census returns, survive for the early Republic through the 1st century CE.[41] Only the figures for periods after the mid-3rd century BCE are reliable, however. Fourteen figures are available for the 2nd century BCE (from 258,318 to 394,736). Only four figures are available for the 1st century BCE, and are feature a large break between 70/69 BCE (910,000) and 28 BCE (4,063,000). The interpretation of the later figures—the Augustan censuses of 28 BCE, 8 BCE, and 14 CE—is therefore controversial.[42] Alternate interpretations of the Augustan censuses (such as those of E. Lo Cascio[43]) produce divergent population histories across the whole imperial period.[44]

Roman population size: the logic of the debate: https://www.princeton.edu/~pswpc/pdfs/scheidel/070706.pdf
- Walter Scheidel (cited in book by Vaclav Smil, "Why America is Not a New Rome")

Our ignorance of ancient population numbers is one of the biggest obstacles to our understanding of Roman history. After generations of prolific scholarship, we still do not know how many people inhabited Roman Italy and the Mediterranean at any given point in time. When I say ‘we do not know’ I do not simply mean that we lack numbers that are both precise and safely known to be accurate: that would surely be an unreasonably high standard to apply to any pre-modern society. What I mean is that even the appropriate order of magnitude remains a matter of intense dispute.

Historical urban community sizes: https://en.wikipedia.org/wiki/Historical_urban_community_sizes

World population estimates: https://en.wikipedia.org/wiki/World_population_estimates
As a general rule, the confidence of estimates on historical world population decreases for the more distant past. Robust population data only exists for the last two or three centuries. Until the late 18th century, few governments had ever performed an accurate census. In many early attempts, such as in Ancient Egypt and the Persian Empire, the focus was on counting merely a subset of the population for purposes of taxation or military service.[3] Published estimates for the 1st century ("AD 1") suggest an uncertainty of the order of 50% (estimates range between 150 and 330 million). Some estimates extend their timeline into deep prehistory, to "10,000 BC", i.e. the early Holocene, when world population estimates range roughly between one and ten million (with an uncertainty of up to an order of magnitude).[4][5]

Estimates for yet deeper prehistory, into the Paleolithic, are of a different nature. At this time human populations consisted entirely of non-sedentary hunter-gatherer populations, with anatomically modern humans existing alongside archaic human varieties, some of which are still ancestral to the modern human population due to interbreeding with modern humans during the Upper Paleolithic. Estimates of the size of these populations are a topic of paleoanthropology. A late human population bottleneck is postulated by some scholars at approximately 70,000 years ago, during the Toba catastrophe, when Homo sapiens population may have dropped to as low as between 1,000 and 10,000 individuals.[6][7] For the time of speciation of Homo sapiens, some 200,000 years ago, an effective population size of the order of 10,000 to 30,000 individuals has been estimated, with an actual "census population" of early Homo sapiens of roughly 100,000 to 300,000 individuals.[8]
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august 2017 by nhaliday
Introduction to Scaling Laws
https://betadecay.wordpress.com/2009/10/02/the-physics-of-scaling-laws-and-dimensional-analysis/
http://galileo.phys.virginia.edu/classes/304/scaling.pdf

Galileo’s Discovery of Scaling Laws: https://www.mtholyoke.edu/~mpeterso/classes/galileo/scaling8.pdf
Days 1 and 2 of Two New Sciences

An example of such an insight is “the surface of a small solid is comparatively greater than that of a large one” because the surface goes like the square of a linear dimension, but the volume goes like the cube.5 Thus as one scales down macroscopic objects, forces on their surfaces like viscous drag become relatively more important, and bulk forces like weight become relatively less important. Galileo uses this idea on the First Day in the context of resistance in free fall, as an explanation for why similar objects of different size do not fall exactly together, but the smaller one lags behind.
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august 2017 by nhaliday
Subgradients - S. Boyd and L. Vandenberghe
If f is convex and x ∈ int dom f, then ∂f(x) is nonempty and bounded. To establish that ∂f(x) ≠ ∅, we apply the supporting hyperplane theorem to the convex set epi f at the boundary point (x, f(x)), ...
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august 2017 by nhaliday
How to estimate distance using your finger | Outdoor Herbivore Blog
1. Hold your right arm out directly in front of you, elbow straight, thumb upright.
2. Align your thumb with one eye closed so that it covers (or aligns) the distant object. Point marked X in the drawing.
3. Do not move your head, arm or thumb, but switch eyes, so that your open eye is now closed and the other eye is open. Observe closely where the object now appears with the other open eye. Your thumb should appear to have moved to some other point: no longer in front of the object. This new point is marked as Y in the drawing.
4. Estimate this displacement XY, by equating it to the estimated size of something you are familiar with (height of tree, building width, length of a car, power line poles, distance between nearby objects). In this case, the distant barn is estimated to be 100′ wide. It appears 5 barn widths could fit this displacement, or 500 feet. Now multiply that figure by 10 (the ratio of the length of your arm to the distance between your eyes), and you get the distance between you and the thicket of blueberry bushes — 5000 feet away(about 1 mile).

- Basically uses parallax (similar triangles) with each eye.
- When they say to compare apparent shift to known distance, won't that scale with the unknown distance? The example uses width of an object at the point whose distance is being estimated.

per here: https://www.trails.com/how_26316_estimate-distances-outdoors.html
Select a distant object that the width can be accurately determined. For example, use a large rock outcropping. Estimate the width of the rock. Use 200 feet wide as an example here.
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august 2017 by nhaliday
How accurate are population forecasts?
2 The Accuracy of Past Projections: https://www.nap.edu/read/9828/chapter/4
good ebook:
Beyond Six Billion: Forecasting the World's Population (2000)
https://www.nap.edu/read/9828/chapter/2
Appendix A: Computer Software Packages for Projecting Population
https://www.nap.edu/read/9828/chapter/12
PDE Population Projections looks most relevant for my interests but it's also *ancient*
https://applieddemogtoolbox.github.io/Toolbox/
This Applied Demography Toolbox is a collection of applied demography computer programs, scripts, spreadsheets, databases and texts.

How Accurate Are the United Nations World Population Projections?: http://pages.stern.nyu.edu/~dbackus/BCH/demography/Keilman_JDR_98.pdf
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july 2017 by nhaliday
Harmonic mean - Wikipedia
The harmonic mean is a Schur-concave function, and dominated by the minimum of its arguments, in the sense that for any positive set of arguments, {\displaystyle \min(x_{1}\ldots x_{n})\leq H(x_{1}\ldots x_{n})\leq n\min(x_{1}\ldots x_{n})} . Thus, the harmonic mean cannot be made arbitrarily large by changing some values to bigger ones (while having at least one value unchanged).

more generally, for the weighted mean w/ Pr(x_i)=t_i, H(x1,...,xn) <= x_i/t_i
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july 2017 by nhaliday
Educational Romanticism & Economic Development | pseudoerasmus
https://twitter.com/GarettJones/status/852339296358940672
deleeted

https://twitter.com/GarettJones/status/943238170312929280
https://archive.is/p5hRA

Did Nations that Boosted Education Grow Faster?: http://econlog.econlib.org/archives/2012/10/did_nations_tha.html
On average, no relationship. The trendline points down slightly, but for the time being let's just call it a draw. It's a well-known fact that countries that started the 1960's with high education levels grew faster (example), but this graph is about something different. This graph shows that countries that increased their education levels did not grow faster.

Where has all the education gone?: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1016.2704&rep=rep1&type=pdf

https://twitter.com/GarettJones/status/948052794681966593
https://archive.is/kjxqp

https://twitter.com/GarettJones/status/950952412503822337
https://archive.is/3YPic

https://twitter.com/pseudoerasmus/status/862961420065001472
http://hanushek.stanford.edu/publications/schooling-educational-achievement-and-latin-american-growth-puzzle

The Case Against Education: What's Taking So Long, Bryan Caplan: http://econlog.econlib.org/archives/2015/03/the_case_agains_9.html

The World Might Be Better Off Without College for Everyone: https://www.theatlantic.com/magazine/archive/2018/01/whats-college-good-for/546590/
Students don't seem to be getting much out of higher education.
- Bryan Caplan

College: Capital or Signal?: http://www.economicmanblog.com/2017/02/25/college-capital-or-signal/
After his review of the literature, Caplan concludes that roughly 80% of the earnings effect from college comes from signalling, with only 20% the result of skill building. Put this together with his earlier observations about the private returns to college education, along with its exploding cost, and Caplan thinks that the social returns are negative. The policy implications of this will come as very bitter medicine for friends of Bernie Sanders.

Doubting the Null Hypothesis: http://www.arnoldkling.com/blog/doubting-the-null-hypothesis/

Is higher education/college in the US more about skill-building or about signaling?: https://www.quora.com/Is-higher-education-college-in-the-US-more-about-skill-building-or-about-signaling
ballpark: 50% signaling, 30% selection, 20% addition to human capital
more signaling in art history, more human capital in engineering, more selection in philosophy

Econ Duel! Is Education Signaling or Skill Building?: http://marginalrevolution.com/marginalrevolution/2016/03/econ-duel-is-education-signaling-or-skill-building.html
Marginal Revolution University has a brand new feature, Econ Duel! Our first Econ Duel features Tyler and me debating the question, Is education more about signaling or skill building?

Against Tulip Subsidies: https://slatestarcodex.com/2015/06/06/against-tulip-subsidies/

https://www.overcomingbias.com/2018/01/read-the-case-against-education.html

https://nintil.com/2018/02/05/notes-on-the-case-against-education/

https://www.nationalreview.com/magazine/2018-02-19-0000/bryan-caplan-case-against-education-review

https://spottedtoad.wordpress.com/2018/02/12/the-case-against-education/
Most American public school kids are low-income; about half are non-white; most are fairly low skilled academically. For most American kids, the majority of the waking hours they spend not engaged with electronic media are at school; the majority of their in-person relationships are at school; the most important relationships they have with an adult who is not their parent is with their teacher. For their parents, the most important in-person source of community is also their kids’ school. Young people need adult mirrors, models, mentors, and in an earlier era these might have been provided by extended families, but in our own era this all falls upon schools.

Caplan gestures towards work and earlier labor force participation as alternatives to school for many if not all kids. And I empathize: the years that I would point to as making me who I am were ones where I was working, not studying. But they were years spent working in schools, as a teacher or assistant. If schools did not exist, is there an alternative that we genuinely believe would arise to draw young people into the life of their community?

...

It is not an accident that the state that spends the least on education is Utah, where the LDS church can take up some of the slack for schools, while next door Wyoming spends almost the most of any state at $16,000 per student. Education is now the one surviving binding principle of the society as a whole, the one black box everyone will agree to, and so while you can press for less subsidization of education by government, and for privatization of costs, as Caplan does, there’s really nothing people can substitute for it. This is partially about signaling, sure, but it’s also because outside of schools and a few religious enclaves our society is but a darkling plain beset by winds.

This doesn’t mean that we should leave Caplan’s critique on the shelf. Much of education is focused on an insane, zero-sum race for finite rewards. Much of schooling does push kids, parents, schools, and school systems towards a solution ad absurdum, where anything less than 100 percent of kids headed to a doctorate and the big coding job in the sky is a sign of failure of everyone concerned.

But let’s approach this with an eye towards the limits of the possible and the reality of diminishing returns.

https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/
https://westhunt.wordpress.com/2018/01/27/poison-ivy-halls/#comment-101293
The real reason the left would support Moander: the usual reason. because he’s an enemy.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/
I have a problem in thinking about education, since my preferences and personal educational experience are atypical, so I can’t just gut it out. On the other hand, knowing that puts me ahead of a lot of people that seem convinced that all real people, including all Arab cabdrivers, think and feel just as they do.

One important fact, relevant to this review. I don’t like Caplan. I think he doesn’t understand – can’t understand – human nature, and although that sometimes confers a different and interesting perspective, it’s not a royal road to truth. Nor would I want to share a foxhole with him: I don’t trust him. So if I say that I agree with some parts of this book, you should believe me.

...

Caplan doesn’t talk about possible ways of improving knowledge acquisition and retention. Maybe he thinks that’s impossible, and he may be right, at least within a conventional universe of possibilities. That’s a bit outside of his thesis, anyhow. Me it interests.

He dismisses objections from educational psychologists who claim that studying a subject improves you in subtle ways even after you forget all of it. I too find that hard to believe. On the other hand, it looks to me as if poorly-digested fragments of information picked up in college have some effect on public policy later in life: it is no coincidence that most prominent people in public life (at a given moment) share a lot of the same ideas. People are vaguely remembering the same crap from the same sources, or related sources. It’s correlated crap, which has a much stronger effect than random crap.

These widespread new ideas are usually wrong. They come from somewhere – in part, from higher education. Along this line, Caplan thinks that college has only a weak ideological effect on students. I don’t believe he is correct. In part, this is because most people use a shifting standard: what’s liberal or conservative gets redefined over time. At any given time a population is roughly half left and half right – but the content of those labels changes a lot. There’s a shift.

https://westhunt.wordpress.com/2018/02/01/bright-college-days-part-i/#comment-101492
I put it this way, a while ago: “When you think about it, falsehoods, stupid crap, make the best group identifiers, because anyone might agree with you when you’re obviously right. Signing up to clear nonsense is a better test of group loyalty. A true friend is with you when you’re wrong. Ideally, not just wrong, but barking mad, rolling around in your own vomit wrong.”
--
You just explained the Credo quia absurdum doctrine. I always wondered if it was nonsense. It is not.
--
Someone on twitter caught it first – got all the way to “sliding down the razor blade of life”. Which I explained is now called “transitioning”

What Catholics believe: https://theweek.com/articles/781925/what-catholics-believe
We believe all of these things, fantastical as they may sound, and we believe them for what we consider good reasons, well attested by history, consistent with the most exacting standards of logic. We will profess them in this place of wrath and tears until the extraordinary event referenced above, for which men and women have hoped and prayed for nearly 2,000 years, comes to pass.

https://westhunt.wordpress.com/2018/02/05/bright-college-days-part-ii/
According to Caplan, employers are looking for conformity, conscientiousness, and intelligence. They use completion of high school, or completion of college as a sign of conformity and conscientiousness. College certainly looks as if it’s mostly signaling, and it’s hugely expensive signaling, in terms of college costs and foregone earnings.

But inserting conformity into the merit function is tricky: things become important signals… because they’re important signals. Otherwise useful actions are contraindicated because they’re “not done”. For example, test scores convey useful information. They could help show that an applicant is smart even though he attended a mediocre school – the same role they play in college admissions. But employers seldom request test scores, and although applicants may provide them, few do. Caplan says ” The word on the street… [more]
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april 2017 by nhaliday
Hoeffding’s Inequality
basic idea of standard pf: bound e^{tX} by line segment (convexity) then use Taylor expansion (in p = b/(b-a), the fraction of range to right of 0) of logarithm
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february 2017 by nhaliday
st.statistics - Lower bound for sum of binomial coefficients? - MathOverflow
- basically approximate w/ geometric sum (which scales as final term) and you can get it up to O(1) factor
- not good enough for many applications (want 1+o(1) approx.)
- Stirling can also give bound to constant factor precision w/ more calculation I believe
- tighter bound at Section 7.3 here: http://webbuild.knu.ac.kr/~trj/Combin/matousek-vondrak-prob-ln.pdf
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february 2017 by nhaliday
Prékopa–Leindler inequality | Academically Interesting
Consider the following statements:
1. The shape with the largest volume enclosed by a given surface area is the n-dimensional sphere.
2. A marginal or sum of log-concave distributions is log-concave.
3. Any Lipschitz function of a standard n-dimensional Gaussian distribution concentrates around its mean.
What do these all have in common? Despite being fairly non-trivial and deep results, they all can be proved in less than half of a page using the Prékopa–Leindler inequality.

ie, Brunn-Minkowski
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february 2017 by nhaliday
bounds - What is the variance of the maximum of a sample? - Cross Validated
- sum of variances is always a bound
- can't do better even for iid Bernoulli
- looks like nice argument from well-known probabilist (using E[(X-Y)^2] = 2Var X), but not clear to me how he gets to sum_i instead of sum_{i,j} in the union bound?
edit: argument is that, for j = argmax_k Y_k, we have r < X_i - Y_j <= X_i - Y_i for all i, including i = argmax_k X_k
- different proof here (later pages): http://www.ism.ac.jp/editsec/aism/pdf/047_1_0185.pdf
Var(X_n:n) <= sum Var(X_k:n) + 2 sum_{i < j} Cov(X_i:n, X_j:n) = Var(sum X_k:n) = Var(sum X_k) = nσ^2
why are the covariances nonnegative? (are they?). intuitively seems true.
- for that, see https://pinboard.in/u:nhaliday/b:ed4466204bb1
- note that this proof shows more generally that sum Var(X_k:n) <= sum Var(X_k)
- apparently that holds for dependent X_k too? http://mathoverflow.net/a/96943/20644
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february 2017 by nhaliday
Energy of Seawater Desalination
0.66 kcal / liter is the minimum energy required to desalination of one liter of seawater, regardless of the technology applied to the process.
infrastructure  explanation  physics  thermo  objektbuch  data  lower-bounds  chemistry  the-world-is-just-atoms  geoengineering  phys-energy  nibble  oceans  h2o  applications  estimate  🔬  energy-resources  biophysical-econ  stylized-facts  ideas  fluid  volo-avolo 
february 2017 by nhaliday
The Brunn-Minkowski Inequality | The n-Category Café
For instance, this happens in the plane when A is a horizontal line segment and B is a vertical line segment. There’s obviously no hope of getting an equation for Vol(A+B) in terms of Vol(A) and Vol(B). But this example suggests that we might be able to get an inequality, stating that Vol(A+B) is at least as big as some function of Vol(A) and Vol(B).

The Brunn-Minkowski inequality does this, but it’s really about linearized volume, Vol^{1/n}, rather than volume itself. If length is measured in metres then so is Vol^{1/n}.

...

Nice post, Tom. To readers whose background isn’t in certain areas of geometry and analysis, it’s not obvious that the Brunn–Minkowski inequality is more than a curiosity, the proof of the isoperimetric inequality notwithstanding. So let me add that Brunn–Minkowski is an absolutely vital tool in many parts of geometry, analysis, and probability theory, with extremely diverse applications. Gardner’s survey is a great place to start, but by no means exhaustive.

I’ll also add a couple remarks about regularity issues. You point out that Brunn–Minkowski holds “in the vast generality of measurable sets”, but it may not be initially obvious that this needs to be interpreted as “when A, B, and A+B are all Lebesgue measurable”, since A+B need not be measurable when A and B are (although you can modify the definition of A+B to work for arbitrary measurable A and B; this is discussed by Gardner).
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february 2017 by nhaliday
Cauchy-Schwarz inequality and Hölder's inequality - Mathematics Stack Exchange
- Cauchy-Schwarz (special case of Holder's inequality where p=q=1/2) implies Holder's inequality
- pith: define potential F(t) = int f^{pt} g^{q(1-t)}, show log F is midpoint-convex hence convex, then apply convexity between F(0) and F(1) for F(1/p) = ||fg||_1
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january 2017 by nhaliday
probability - How to prove Bonferroni inequalities? - Mathematics Stack Exchange
- integrated version of inequalities for alternating sums of (N choose j), where r.v. N = # of events occuring
- inequalities for alternating binomial coefficients follow from general property of unimodal (increasing then decreasing) sequences, which can be gotten w/ two cases for increasing and decreasing resp.
- the final alternating zero sum property follows for binomial coefficients from expanding (1 - 1)^N = 0
- The idea of proving inequality by integrating simpler inequality of r.v.s is nice. Proof from CS 150 was more brute force from what I remember.
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january 2017 by nhaliday
cv.complex variables - Absolute value inequality for complex numbers - MathOverflow
In general, once you've proven an inequality like this in R it holds automatically in any Euclidean space (including C) by averaging over projections. ("Inequality like this" = inequality where every term is the length of some linear combination of variable vectors in the space; here the vectors are a, b, c).

I learned this trick at MOP 30+ years ago, and don't know or remember who discovered it.
q-n-a  overflow  math  math.CV  estimate  tidbits  yoga  oly  mathtariat  math.FA  metabuch  inner-product  calculation  norms  nibble  tricki 
january 2017 by nhaliday
Borel–Cantelli lemma - Wikipedia
- sum of probabilities finite => a.s. only finitely many occur
- "<=" w/ some assumptions (pairwise independence)
- classic result from CS 150 (problem set 1)
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november 2016 by nhaliday
Faster than Fisher | West Hunter
There’s a simple model of the spread of an advantageous allele:  You take σ, the typical  distance people move in one generation, and s,  the selective advantage: the advantageous allele spreads as a nonlinear wave at speed  σ * √(2s).  The problem is, that’s slow.   Suppose that s = 0.10 (a large advantage), σ = 10 kilometers, and a generation time of 30 years: the allele would take almost 7,000 years to expand out 1000 kilometers.

...

This big expansion didn’t just happen from peasants marrying the girl next door: it required migrations and conquests. This one looks as if it rode with the Indo-European expansion: I’ll bet it started out in a group that had domesticated only horses.

The same processes, migration and conquest, must explain the wide distribution of many geographically widespread selective sweeps and partial sweeps. They were adaptive, all right, but expanded much faster than possible from purely local diffusion. We already have reason to think that SLC24A5 was carried to Europe by Middle Eastern farmers; the same is probably true for the haplotype that carries the high-activity ergothioniene transporter and the 35delG connexin-26/GJB2 deafness mutation. The Indo-Europeans probably introduced the T-13910 LCT mutation and the delta-F508 cystic fibrosis mutation, so we should see delta-F508 in northwest India and Pakistan – and we do !

https://westhunt.wordpress.com/2014/11/22/faster-than-fisher/#comment-63067
To entertain a (possibly mistaken) physical analogy, it sounds like you’re suggested a sort genetic convection through space, as opposed to conduction. I.e. Entire masses of folks, carrying a new selected variant, are displacing others – as opposed to the slow gene flow process of “girl-next-door.” Is that about right? (Hopefully I haven’t revealed my ignorance of basic thermodynamics here…)

Has there been any attempt to estimate sigma from these time periods?

Genetic Convection: https://westhunt.wordpress.com/2015/02/22/genetic-convection/
People are sometimes interested in estimating the point of origin of a sweeping allele: this is probably effectively impossible even if diffusion were the only spread mechanism, since the selective advantage might well vary in both time and space. But that’s ok, since population movements – genetic convection – are real and very important. This means that the difficulties in estimating the origin of a Fisher wave are totally insignificant, compared to the difficulties of estimating the effects of past colonizations, conquests and Völkerwanderungs. So when Yuval Itan and Mark Thomas estimated that 13,910 T LCT allele originated in central Europe, in the early Neolithic, they didn’t just go wrong because of failing to notice that the same allele is fairly common in northern India: no, their whole notion was unsound in the first place. We’re talking turbulence on steroids. Hari Seldon couldn’t figure this one out from the existing geographic distribution.
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november 2016 by nhaliday
Bounds on the Expectation of the Maximum of Samples from a Gaussian
σ/sqrt(pi log 2) sqrt(log n) <= E[Y] <= σ sqrt(2) sqrt(log n)

upper bound pf: Jensen's inequality+mgf+union bound+choose optimal t (Chernoff bound basically)
lower bound pf: more ad-hoc (and difficult)
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october 2016 by nhaliday
Overcoming Bias : In Praise of Low Needs
We humans have come a long way since we first became human; we’ve innovated and grown our ability to achieve human ends by perhaps a factor of ten million. Not at all shabby, even though it may be small compared to the total factor of growth and innovation that life achieved before humans arrived. But even if humanity’s leap is a great achievement, I fear that we have much further to go than we have come.

The universe seems almost entirely dead out there. There’s a chance it will eventually be densely filled with life, and that our descendants may help to make that happen. Some worry about the quality of that life filling the universe, and yes there are issues there. But I worry mostly about the difference between life and death. Our descendants may kill themselves or stop growing, and fail to fill the universe with life. Any life.

To fill the universe with life requires that we grow far more than our previous leap factor of ten million. More like three to ten factors that big still to go. (See Added below.) So think of all the obstacles we’ve overcome so far, obstacles that appeared when we reached new scales of size and levels of ability. If we were lucky to make it this far, we’ll have to be much more lucky to make it all the way.

...

Added 28Oct: Assume humanity’s leap factor is 107. Three of those is 1021. As there are 1024 stars in observable universe, that much growth could come from filling one in a thousand of those stars with as many rich humans as Earth now has. Ten of humanity’s leap is 1070, and there are now about 1010 humans on Earth. As there are about 1080 atoms in the observable universe, that much growth could come from finding a way to implement one human like creature per atom.
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october 2016 by nhaliday
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